How exactly is "za" translated here?
You cannot translate every word. Different verbs have different kind of valences in different languages. "to consider somebody something" is "považovat někoho za něco". It is just a preposition used with the verb.
In this case, does "za" require accusative or genitive?
accusative, genitive would be něčeho, not něco
Does 'za' always accompany 'považovat'?
Yes, but there is also "považovat si" which means something else and is used differently.
I just got a typo when I wrote "považuji" instead of "považuje". But as far as I know both answers are correct and are just equivalent forms
považuje is wrong. You need považuju or považuji, both are correct. Not equivalent though, považuji is formal.